Subtract $4p^2-9p+11$ from $p^2-5p+4$.
Since we are asked to subtract $4p^2-9p+11$ from $p^2-5p+4$, let's rewrite it as one expression. But how do we know which terms go where? Well, if we were asked to "subtract $2$ from $5$ ", we would rewrite it as $5 - 2$. In other words, we would start with $5$ and then subtract $2$. Let's use this pattern to rewrite the problem as one expression: ${(p^2-5p+4)-(4p^2-9p+11)}$ Since we are subtracting, it is helpful to distribute the $\text{{negative sign}}$ across all terms in the second trinomial: $\begin{aligned}&(p^2-5p+4){-}(4p^2-9p+11)\\ \\ =&(p^2-5p+4){-}4p^2{-}(-9p){-}11\\ \\ =&p^2-5p+4-4p^2+9p-11 \end{aligned}$ Note that the parentheses around the first trinomial don't affect the order of operations, so we can just remove them. When we add or subtract terms in a polynomial expression, the only way that we can simplify the expression is by combining those terms that are alike. Our expression contains terms of $3$ different degrees in the same variable: ${p^2}, {p},$ and the $\text{{constant}}$ term: ${{p^2} {-5p} {+4} {-4p^2} {+9p} {-11}}$ Note that there is an "invisible" coefficient of $1$ in front of the term ${p^2}$. Now that we have identified like terms, let's combine them. Make sure to keep track of positive and negative signs! ${{(1-4)p^2} + {(-5+9)p} + {(4-11)}}$ When we combine the coefficients in front of each term, we get the following trinomial: ${-3p^2+4p-7}$